I use oxy/acetylene because it burns really hot, and have never tried silver soldering with Mapp gas by itself. Mapp gas paired with oxygen would be certainly work. Whatever you use has to heat the tubing, patch, and the silver so that the silver will flow along the tubing and under the patch.
I've heard that straight Mapp gas will work with silver solder only if you are using the lower melting point type of silver solder - which is called "low" or "easy" sillver solder -and forms a brazed bond at about 1400 F. But that should work.
BTW, silver soldering is really a type of brazing. It is not at all like tin alloy plumber's solder which flows at 400 to 600 F. I don't know why "silver brazing" ever got to be called "silver soldering", but it is.
Might as well get some scrap and practice first. It is often easiest to silver braze a patch made of a split piece of similar size tubing onto the hydraulic tubing. You might even try some copper tubing for the patch. Make it fit really well and clean and flux the cleaned metal before brazing it. Or you could get some copper wire and wind it around the tubing and then flow the solder onto that wire. With clean copper, flux, and enough heat the silver should wick along the tube and under the patch and all but disappear. If it flows that nicely, you know the joint is good. The patch helps reinforce the silver. It is easier to patch tubing than to try to just cover a split with solder.
Silver solder rod and flux is kinda expensive.
If you know a refrigeration repair shop, they tend to use a lot of silver solder & might sell you a single rod. Get a lump of their brazing flux, too. You can mix the flux with water if it dries out. I think the leak is right at the line to fitting connection. It's a tiny leak - a drip every 5s.
rScotty